Structure of the hydrogen double vacancy on Pd(111)

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We determine the ground-state structure of a double vacancy in a hydrogen monolayer on the Pd(111) surface. We represent the double vacancy as a triple vacancy containing one additional hydrogen atom. The potential-energy surface for a hydrogen atom moving in the triple vacancy is obtained by density-functional theory, and the wave function of the fully quantum hydrogen atom is obtained by solving the Schr\"odinger equation. We find that an H atom in a divacancy defect experiences significant quantum effects, and that the ground-state wave function is centered at the hcp site rather than the fcc site normally occupied by H atoms on Pd(111). Our results agree well with scanning tunneling microscopy images. Full Article:


Fig. 1. Minimum potential-energy surface for a hydrogen atom in a divacancy. The minimum potential energy in the z direction for all points in the xy plane of a single classical H atom moving in a three site cluster. Large and small white circles representing top layer Pd atoms and neighboring H atoms, respectively, are drawn as visual guides. The color bar shows corresponding potential values in eV.

Understanding the fundamental mechanisms that govern the behavior of hydrogen on metal surfaces is important to new technologies involving hydrogen production, storage, and energy conversion. Because of its light mass, hydrogen can manifest uniquely quantum effects not seen for other elements. These effects can have striking consequences when the dimensionality of the allowed motion is constrained by adsorption on a surface. When a metal surface such as palladium is covered by a nearly complete monolayer of hydrogen, small clusters of vacancies in the hydrogen layer serve as active sites for the dissociative adsorption of additional H2 molecules. Despite their central role in catalysis, the exact nature of these vacancy defects is not well understood. It has been generally accepted that the dissociative adsorption of the diatomic molecule H2 is to require at least two adjacent and empty atomic adsorption sites (or vacancies ) based on early studies of Conrad et al. and Langmuir. Recently, intriguing observations about hydrogen divacancies on palladium were made using scanning tunneling microscopy (STM). Mitsui et al. reported that hydrogen molecules impinging on an almost H-saturated Pd(111) surface did not adsorb in two-vacancy sites. Rather, aggregates of three or more hydrogen vacancies were required for efficient dissociation of H2 molecules. These findings led to speculations that the standard description from Langmuir adsorption kinetics11 might be too simple to explain the dissociative adsorption of hydrogen on Pd(111).

Minimum potential-energy surface

Fig. 2. Wave functions of a H atom in a divacancy. Isosurface of the real component of the wave functions of a hydrogen atom in a structure used to simulate a 2Vq vacancy defect that contains three fcc sites and one hcp site. The isovalues on red surfaces are positive, while the values on blue surfaces are negative. All imaginary components are zero.

Figure 1 shows the minimum PES for a hydrogen atom in a 3VH defect. Two important conclusions can be drawn from this energy surface. First, the only low-energy pathways available to the hydrogen atom are those connecting the three fcc sites to central hcp site. Second, there are no low-energy pathways available to allow the surrounding hydrogen atoms to move into the vacancy region. The region of low potential (blue and green) is surrounded by neighboring H atoms and by construction possesses C3v symmetry about the central hcp site. The potential floor (blue) region has three branches extending from the central hcp site to fcc sites, where the potential reaches its minimum. The local minimum at the hcp site is 20 meV higher than that at the fcc sites.

Wave functions of a H atom in a divacancy

The results of our calculations for the low-energy eigenstates are summarized in Table I and their wave functions are shown in Fig. 1. Of particular interest is the ground state , which is localized at the hcp site. We note that this is not the minimum of the potential-energy surface which occurs at the fcc sites. If the H atom had been treated classically, the ground-state configuration would have the H atom adsorbed at the fcc site, corresponding to the defect configuration 2Vc.


We have studied the quantum nature of hydrogen atoms on Pd(111) surface by solving the Schrödinger equation for a H atom moving in static potential-energy surface determined from first-principles density-functional theory calculations. We find that a H atom in a divacancy defect experiences significant quantum effects, with the result that its wave functions are extended over large portion of the vacancy. The ground-state H wave function is centered at an hcp site rather than the fcc site occupied by classical H atoms. As a result, the divacancy should exhibit a triangular geometry with threefold symmetry, consistent with recent experiments.

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